|Asymptotic Behavior Analysis of a Heat Equation Coupled with a Fractional Ordinary Differential System
Mimi Hou, Xuan-Xuan Xi, and Xian-Feng Zhou*
International Journal of Control, Automation, and Systems, vol. 20, no. 10, pp.3155-3166, 2022
Abstract : This paper considers the existence, uniqueness and the asymptotic behavior of a classic heat equation coupled with a fractional ordinary differential system. By the Lumer-Phillips theorem, we obtain the existence and uniqueness of the solution. Furthermore, we use a new Lyapunov functional to show the global attractivity for the considered system, then the tractable global attractive conditions are obtained. Finally, numerical examples are provided to illustrate the applications of our results.
Coupled system, global attractivity, Lyapunov functional, Riemann-Liouville derivatives.